Question

An object is observed to move under the following equation of motion ... x(t) = A√t ... take A =√2. Determine the equations for the velocity and acceleration as a function of time. Write each equation in differential equation format, including second-order, if necessary.

Answer 1

Explanation:

x(t) = A√t

x(t) = √(2t)

v(t) = dx/dt

v(t) = ½ (2t)^-½ × 2

v(t) = (2t)^-½

a(t) = dv/dt

a(t) = -½ (2t)^⁻³/₂ × 2

a(t) = -(2t)^⁻³/₂